Inhomogeneity And Anisotropic Study On Microscale Mechanical Behavior Of Lead-Free Solders In Electronic Packaging

The failure of electronic products is mostly caused by the failure of solder joints.The accurate description of the mechanical behavior of solder joints under the microscopic condition is the premise to improve the reliability of solder joints,which is of great significance to improve the quality of electronic products.With the continuous development of high-density electronic packaging technology,the size of solder joints is gradually reduced to the micron level.The phase distribution and mechanical anisotropy in the solder matrix are obvious,so the classical mechanical theory and isotropic hypothesis of homogeneous material can not be used to evaluate the reliability.In this paper,the mechanical behavior of the eutectic structure of Sn58 Bi solder matrix was studied by the first-principles calculation,nano indentation test and finite element inversion analysis,as well as the finite element analysis based on Monte Carlo method.Firstly,the mechanical properties of Sn and Bi were studied by the first principle method.The elastic constants of Sn and Bi single crystals are calculated,the calculated results are close to the experimental values.On this basis,the polycrystalline mechanical properties of Sn and Bi are calculated.The elastic modulus and Poisson's ratio are close to the experimental value,which verified the accuracy of the theoretical values.In addition,the general anisotropy index and elastic modulus anisotropy of Sn and Bi show that they are anisotropic.Then,the hardness,elastic modulus,Poisson's ratio and load displacement curves of Sn and Bi were obtained by nanoindentation experiment.The characteristic stress,strain strengthening coefficient,characteristic strain and yield strength of Sn and Bi were determined according to the dimension theory of nano-indentation process,and the theoretical yield strength of Sn is close to that of the tensile test.The displacement load curve obtained by the inversion is consistent with the experimental curve,which verifies the effectiveness of the Sn and Bi inversion analysis.In addition,the stress-strain curve equations of Sn and Bi are obtained.Finally,based on the monte carlo method,the finite element model of heterogeneous distribution of Sn and Bi phases is established.On this basis,the elastoplastic mechanical behavior of the indenter pressed into Sn58 Bi eutectic microstructure under anisotropy was studied.It is found that the inhomogeneous distribution of the phases has the greatest influence on the first principal stress of the Bi and Sn rich phases,the smallest influence on the maximum shear stress of the Sn rich phase,and the smallest influence on the equivalent stress of the Bi rich phase.In the case of relative isotropy,anisotropy has different degrees of influence on the maximum principal stress,maximum shear stress,equivalent stress and damage equivalent stress of Sn58 Bi.The most affected is the equivalent stress and the least affected is the maximum shear stress.The results also found that the average stress of Sn58 Bi anisotropy was higher than that of the isotropy.It is inferred that the Sn rich phase is the weaker part of Sn58 Bi eutectic structure.In addition,the mean stress values of Sn58 Bi in different material orientations are different,and the mean stress values are larger than those in the case of isotropy,which shows that the inhomogeneous distribution and anisotropy of the phase affect the mechanical properties of the eutectic structure.